A Measure-Valued Approach to Convex Set-Valued Dynamics
Copyright policy )A Measure-Valued Approach to Convex Set-Valued Dynamics
A new approach to the evolution of convex-valued multifunctions is presented, analogous to single-valued gradient dynamics. Simple convex-valued multifunctions are introduced to approximate the solution of a convex-valued differential equation; then the differentiability of these multifunctions is investigated. A constraint stochastic optimization problem is also presented. The approach to set-valued differentiation developed in this paper essentially differs from existing ones and thus may be a fruitful source of open problems for further research.
- University of Vienna Austria
Abstract differentiation theory, differentiation of set functions, Differential equations in abstract spaces, convex-valued dynamics, differentiable multifunction, dynamical systems, Mixed volumes and related topics in convex geometry, Nonparametric hypothesis testing, Set-valued maps in general topology, constraint optimization
Abstract differentiation theory, differentiation of set functions, Differential equations in abstract spaces, convex-valued dynamics, differentiable multifunction, dynamical systems, Mixed volumes and related topics in convex geometry, Nonparametric hypothesis testing, Set-valued maps in general topology, constraint optimization
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!